How to prove gravitational force inside a hollow sphere is zero?

Asked Dec 08 '20 at 05:55

Active Dec 08 '20 at 05:55

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I'm just trying to prove that gravitational force on an object within a hollow sphere is zero when these are the only two objects under consideration within the system.

I know some multivariable calculus, I just want someone to walk me through the integration deriving the mass element dM and the integration of thin rings composing the hollow sphere. It would also be nice if you could show me doing it one way using the solid angle and one way without using the solid angle. Thanks.

asked Dec 08 '20 at 05:55

CalebWilliamsUIC

2

Does this answer your question? Gravitational field intensity inside a hollow sphere – Nihar Karve Dec 08 '20 at 06:06
1

It’s easier to do the integral for the gravitational potential and show that it is uniform inside. This means that the field (the gradient of the potential) is zero. – G. Smith Dec 08 '20 at 07:10
@G.Smith I see. I would have to find the potential function. – CalebWilliamsUIC Dec 08 '20 at 07:16
Related : Would you be weightless at the center of the Earth?. – Frobenius Dec 08 '20 at 20:29

How to prove gravitational force inside a hollow sphere is zero?

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